Prescription-dependent and individualization-dependent modification of the temporal peripheral nominal astigmatism and adaption of the object distance function to changed object distances for near and/or far vision

ABSTRACT

Method for optimization of a progressive spectacle lens, which method comprises: defining a starting nominal astigmatism distribution for the spectacle lens; determining a transformed nominal astigmatism distribution and optimizing the spectacle lens on the basis of the transformed nominal astigmatism distribution, wherein the determination of a transformed nominal astigmatism distribution comprises multiplication of the maximum temporal nominal astigmatism of the starting nominal astigmatism distribution by a factor k as a result of which a modified maximum temporal astigmatism is obtained, wherein k is a function of a prescription value, and/or at least of one parameter of the spectacle lens or of the arrangement thereof in front of the eyes, and transformation of the starting nominal astigmatism distribution on the basis of the modified maximum temporal astigmatism.

BACKGROUND

Aspects of the present invention relate to a computer-implemented methodfor optimizing and producing a progressive spectacle lens, correspondingdevices for optimizing and producing a progressive spectacle lens,corresponding computer program products and storage media, as well as toa use of a spectacle lens.

An optimization of a progressive spectacle lens is usually performed byminimizing a target function in which required or target values for atleast one optical parameter, e.g. astigmatism and/or refractive power,or required or target values for at least one aberration, e.g.astigmatic error and/or refractive error, of the progressive spectaclelens are taken into account. In the optimization process of thespectacle lens, the individual prescription values (sph, cyl, axis, add,prism, base), parameters of the individual position or arrangement ofthe spectacle lens in front of the spectacles wearer's eye (e.g. cornealvertex distance (CVD), face form angle (FFA), forward inclination orpantoscopic angle), as well as physiological parameters (e.g. pupillarydistance) can be taken into account. The progressive spectacle lens canbe optimized and calculated “online” as one-of-a-kind after receipt oforder.

Moreover, DE 10 2008 015 189, DE 10 2009 005 206, or DE 10 2009 005 214suggest determining the target astigmatism distribution, on the basis ofwhich the progressive spectacle lens is optimized, by means of atransformation of an existing or predetermined design (starting design,base design). For example, DE 10 2008 015 189 suggests calculatingtarget astigmatism distributions for different additions by means of atransformation of a predetermined base or starting target astigmatismdistribution, which has been specified for a predetermined baseaddition. DE 10 2009 005 206 and DE 10 2009 005 214 suggest creatingtarget astigmatism distributions with different widths of the distanceand/or near zone(s) from a predetermined target astigmatism distributionby means of manipulation of a predetermined base target astigmatismline. The methods described in DE 10 2008 015 189, DE 10 2009 005 206,or DE 10 2009 005 214 make it possible to simplify the method foroptimizing and producing a progressive spectacle lens and making it moreefficient and flexible.

SUMMARY

It is an object of the invention to provide improved methods foroptimizing and producing progressive spectacle lenses.

This object is solved by a computer-implemented method for optimizing aprogressive spectacle lens, a computer program product, a storage mediumwith a computer program stored thereon, a device for optimizing aprogressive spectacle lens, a method for producing a progressivespectacle lens, a device for producing a progressive spectacle lens, anda use of a spectacle lens.

A first aspect of the invention relates to a computer-implemented methodfor optimizing a progressive spectacle lens, comprising the steps of:

-   -   specifying a starting target astigmatism distribution        Ast_(target) _(start) for the progressive spectacle lens;    -   determining a transformed target astigmatism distribution        Ast_(target) _(new) , and    -   optimizing the progressive spectacle lens on the basis of the        transformed target astigmatism distribution.

Determining a transformed target astigmatism distribution Ast_(target)_(new) comprises the steps of:

-   -   multiplying the value of the maximum temporal target astigmatism        max_Ast_(target—)temporal_(start) of the starting target        astigmatism distribution Ast_(target) _(start) by a factor k:    -   max_(—) Ast _(target—)temporal_(new) =k*max_(—) Ast        _(target—)temporal_(start),    -   whereby a modified maximum temporal astigmatism        max_Ast_(target—)temporal_(new) results, wherein the factor k is        a function of at least one prescription value and/or of at least        one parameter of the spectacle lens or its arrangement in front        of the eyes of the spectacles wearer; and    -   transforming the starting target astigmatism distribution        Ast_(target) _(start) on the basis of the modified maximum        temporal astigmatism max_Ast_(target—)temporal_(new).

As mentioned above, the optimization of progressive spectacle lenses isusually performed by iteratively minimizing a target function in whichrequired or target values for at least one optical parameter (e.g.astigmatism and/or refractive power) or required or target values for atleast one aberration (e.g. astigmatic error and/or refractive error) ofthe progressive spectacle lens are taken into account. The refractiveerror represents the difference of the refractive power of the spectaclelens to the refractive power determined by means of refractiondetermination. Preferably, these are values in the wearing position ofthe spectacle lens, i.e. taking the system spectacle lens-eye intoaccount. The degree of freedom in the optimization of the targetfunction is usually the vertex depth of the front surface or backsurface of the spectacle lens, or of both the front and back surfaces,e.g. in the case of a double progressive spectacle lens.

For example, a design-based optimization of a progressive spectacle lenscan be performed by minimizing a target function of the form:

$\begin{matrix}{{F\left( \overset{\rightarrow}{x} \right)} = {\sum\limits_{i = 1}^{m}\;\left\lbrack {{g_{i,{Ast}}\left( {{Ast}_{i} - {Ast}_{i,{target}}} \right)}^{2} + \ldots} \right\rbrack}} & (1)\end{matrix}$or of the form:

$\begin{matrix}{{F\left( \overset{\rightarrow}{x} \right)} = {\sum\limits_{i = 1}^{m}\;\left\lbrack {{g_{i,{\Delta\; R}}\left( {{\Delta\; R_{i}} - {\Delta\; R_{i,{target}}}} \right)}^{2} + {g_{i,{Ast}}\left( {{Ast}_{i} - {Ast}_{i,{target}}} \right)}^{2} + \ldots} \right\rbrack}} & (2)\end{matrix}$In the above formula:

-   ΔR_(i,target) is the target value of the local refractive    error/refractive power at the i^(th) evaluation point;-   ΔR_(i) is the actual local refractive error/refractive power at the    i^(th) evaluation point;-   Ast_(i,target) is the target value of the local astigmatic    error/astigmatism at the i^(th) evaluation point;-   Ast_(i) is the actual local astigmatic error/astigmatism at the    i^(th) evaluation point;-   g_(i,ΔR) is the local weighting of the refractive error/refractive    power at the i^(th) evaluation point;-   g_(i,Ast) is the local weighting of the astigmatic error/astigmatism    at the i^(th) evaluation point.

The actual and target values of the at least one optical property, whichare taken into account in the target function, may be both target values(surface values or values in the wearing position) of the spectacle lensand target values for at least one aberration. Within the scope of thisapplication, the term “target astigmatism” is understood to mean boththe astigmatism of the spectacle lens (as surface power or in thewearing position) and the astigmatic error. Moreover, the term “targetastigmatism distribution” within the scope of this application isunderstood to mean both the spatial distribution of the target values ofthe astigmatism of the spectacle lens and the spatial distribution ofthe target values of the astigmatic error. The target values of the atleast one optical property of the spectacle lens and in particular thetarget values of the astigmatism or the astigmatic error characterizedthe “design” of a spectacle lens. In addition, the spectacle lens designcan comprise a suitable object distance model. The object distance modelmay comprise an object distance function, which is defined as thereciprocal object distance along the main line of sight. A standardizedobject distance model is indicated in DIN 58 208 part 2 (cf. image 6),for example. However, the object distance model may be different fromthis standardized object distance model.

The target astigmatism distribution, on the basis of which theprogressive spectacle lens is optimized, can be obtained by means of atransformation of an existing or predetermined design (starting design,base design). For example, DE 10 2008 015 189 suggests obtaining targetastigmatism distributions for different additions by means of atransformation of a predetermined base or starting target astigmatismdistribution, which has been defined for a predetermined base addition.DE 10 2009 005 206 or DE 10 2009 005 214 suggest creating targetastigmatism distributions with different widths of the distance and/ornear zone(s) from a predetermined target astigmatism distribution bymeans of manipulation of a predetermined base target astigmatism line.The power dependency of the target astigmatism can be satisfied withdifferent base designs.

The starting design (base design) usually exhibits an almost symmetricdistribution of the target astigmatism with respect to the main line ofsight due to the binocular image formation properties. In an additionand/or power and/or progression length-dependent transformation of thestarting design, the almost symmetric distribution of the targetastigmatism is substantially maintained.

However, according to a first aspect of the invention, it has been foundthat for certain combinations of prescription values and/or parametersof the spectacle lens and/or its arrangement in front of the eyes of thespectacles wearer (i.e. is wearing position), the above-describedprocedure, in which the target astigmatism distribution taken intoaccount in the target function is almost symmetric with respect to themain line of sight, can lead to suboptimal results. For example, thegradients of the surface properties of the progressive surface and/orthe gradients of the “as worn” power are often relatively large. Thisresults in deteriorated wearing position properties of the spectaclelens (astigmatism and/or refractive power in wearing position of thespectacle lens).

These disadvantages arise particularly in the case of spectacle lenseshaving a flat base curve (i.e. a base curve in the range of 0 dpt to 4dpt) and higher back surface curvatures (i.e. back surface curvaturesequal to or greater than −6 dpt), especially in combination with:

-   -   high prescription cylinders, i.e. cylinders in the range of        equal to or greater than 2 dpt, and/or    -   oblique cylinders axis positions of the prescription cylinder,        i.e. cylinder axis positions of the prescription cylinder from 0        to 90° according to TABO (technical committee for eyewear        optics) for right spectacle lenses, and from 90 to 180° for left        spectacle lenses; and/or    -   a small prescription addition, i.e. an addition of <2.0 dpt,        preferable and addition of ≦1.5 dpt,    -   and/or in combination with larger tilt angles of the spectacle        lens in front of the eye, i.e. tilt angles in the range equal to        or larger than 5°.

It has been found that one reason for the occurrence of higher gradientsof the surface properties for spectacle lenses exhibiting one of theabove combinations is the systematic distribution of the targetastigmatism with respect to the main line of sight. For example, in thecase of a toric overlay of a predetermined starting surface with atoroidal or atoroidal surface, an astigmatic error may occur temporally,which is partly clearly below the value of the target astigmatismaccording to the symmetric target astigmatism distribution. However, theoptimization process tries to achieve the symmetric objectives for thetarget astigmatism and therefore “bends” the surface to be optimizedmore strongly at this point as would be required for low additions.

According to the first aspect of the invention, it is thereforesuggested that the temporal target astigmatism in the periphery of thespectacle lens be multiplied by a factor k to take these facts intoaccount. The factor k will preferably have the value 1 if the targetastigmatism values are not to be manipulated, and a value of smallerthan 1 if the target astigmatism values are to be manipulated. Thefactor k is a function of at least one prescription value (such assphere, cylinder, cylinders axis, prism, prism base and/or addition)and/or of at least one parameter of the spectacle lens or itsarrangement in front of the eyes of the spectacles wearer (i.e. itswearing position). The parameters of the spectacle lens and/or itsarrangement in front of the eyes of the spectacles wearer (i.e. itswearing position) are e.g. the face form angle, the tilt angle, thecorneal vertex distance (CVD), forward inclination or pantoscopic angle,the interpupillary distance, the ocular center of rotation distanceand/or other parameters. These may be average values (as defined in DIN58 208 part 2, for example) or values determined individually for aspecific spectacles wearer.

Specifically, it is suggested that the maximum temporal targetastigmatism max_Ast_(target—)temporal_(start) (which usually occurs inthe periphery of the spectacle lens) of the predetermined startingtarget astigmatism distribution Ast_(target,start) be multiplied by afactor k, whereby a new, transformed, maximum temporal astigmatismmax_Ast_(target—)temporal_(new) results:max_(—) Ast _(target—)temporal_(new) =k*max_(—) Ast_(target—)temporal_(start).  (3)

The starting target astigmatism distribution Ast_(start) across thespectacle lens can be the target astigmatism distribution of apredetermined progressive starting surface. Alternatively, it ispossible to specify a target astigmatism model on the basis of which thestarting target astigmatism distribution can be calculated. The targetastigmatism model may be the target astigmatism model described in DE 102008 015 189, DE 10 2009 005 206, or DE 10 2009 005 214. In particular,the course of a main line and the course of at least one base targetisoastigmatism line can be specified parametrically or numerically. Alltarget astigmatism values between the main line and the base targetisoastigmatism line as well as all target astigmatism values between thebase target isoastigmatism line and the periphery of the spectacle lenscan be determined subsequently by means of a suitable interpolation(e.g. a linear, quadratic, cubic interpolation) of the predeterminedtarget astigmatism values on the main line and the base targetisoastigmatism line, and optionally other predetermined values, asdescribed in DE 10 2009 005 206 or DE 10 2009 005 214.

In a next step, a new, transformed target astigmatism distributionAst_(target) _(new) is determined on the basis of the new, transformed,maximum temporal astigmatism. Here, preferably, the nasal targetastigmatism values or the nasal target astigmatism distribution remainunchanged.

The new, transformed target astigmatism distribution Ast_(target) _(new)can be obtained by multiplying all temporal values of the targetastigmatism (i.e. all target astigmatism values on the temporal side ofthe main line of sight) by the factor k:Ast _(target) _(new) _temporal=k*Ast _(target) _(start) _temporal.  (4)

According to a preferred embodiment, however, a new, transformed targetastigmatism distribution Ast_(target) _(new) is obtained by means of aninterpolation of the target astigmatism values between a predeterminedtemporal base target isoastigmatism line (usually the 0.5 dpt basetarget isoastigmatism line) and the periphery of the spectacle lens,wherein the modified value of the maximum temporal astigmatismmax_Ast_(target—)temporal_(new) is taken into consideration. Thedocuments DE 10 2009 005 206 or DE 10 2009 005 214 each describe amethod (parallel curve model method or truncated cone model method) forcalculating a target astigmatism distribution on the basis of apredetermined base target isoastigmatism line and the maximum, temporalastigmatism. The predetermined 0.5 dpt base target isoastigmatism linecan be determined on the basis of the starting target astigmatismdistribution. Here, preferably, the temporal target astigmatism valuesbetween the main line and the temporal base target isoastigmatism lineremain unchanged. In addition to a low value of the maximum temporaltarget astigmatism, the new, transformed target astigmatism distributionusually exhibits smaller gradients of the target astigmatism in theperiphery.

Preferably, transforming the starting target astigmatism distributionAst_(target) _(start) on the basis of the modified maximum temporalastigmatism max_Ast_(target—)temporal_(new) consequently comprises aninterpolation of the target astigmatism values between a predeterminedbase target isoastigmatism line and the periphery of the spectacle lenstaking the modified maximum temporal astigmatismmax_Ast_(target—)temporal_(new) into account.

The optimization objectives for the spectacle lens, including thestarting target astigmatism distribution and the transformed targetastigmatism distribution Ast_(target) _(new) , can be indicated in asuitable coordinate system.

An exemplary coordinate system is a coordinate system in the object-sideor eye-side surface of the spectacle lens to be optimized, wherein theorigin of the coordinate systems e.g. coincides with the geometriccenter of the raw-round spectacle lens or with the centration or fittingpoint of the spectacle lens. The vertical (“y”) and horizontal (“x”)axes lie in the tangential plane with respect to the respective eye-sideor object-side surface of the spectacle lens in the geometric center orthe centration or fitting point. The vertical direction preferablyrefers to the vertical direction in the wearing position of thespectacle lens, wherein the spectacle lens is for example arranged in anaverage wearing position (as defined e.g. in DIN 58 208 part 2) or in anindividual wearing position. Preferably, the spectacle lens is arrangedin an individual wearing position. In this coordinate system,Ast_(target) _(start) =Ast_(target) _(start) (x,y) and Ast_(target)_(new) =Ast_(target) _(new) (x,y) apply.

Of course, it is possible to indicate the spatial distribution of theaberrations in other suitable coordinate systems.

It is particularly preferred to indicate the target astigmatism valuesand the optimization values in the coordinate system of the surface tobe optimized with respect to the main line or the main line of sight(where u=0 applies on the main line/main line of sight), and not withrespect to the y axis (x=0), i.e. in the form Ast_(target) _(start)=Ast_(target) _(start) (u,y), Ast_(target) _(new) =Ast_(target) _(new)(u,y). If the target values or optimization values are specified withrespect to the main line, it will be sufficient, in the case changingthe wearing position of the spectacle lens to be taken intoconsideration, and in particular in the case of changing theinterpupillary distance, the corneal vertex distance, the forwardinclination, the object distance model, etc., to merely match the mainline to the modified main line of sight. The target values oroptimization target values are automatically adjusted then.

The factor k, which is also referred to as a multiplication factor, canbe calculated as follows:k=(1−g _(prescription) −h),  (5)where

-   g_(prescription) is a function of at least one prescription value,    and-   h is a function of at least one (individual) parameter of the    spectacle lens or its arrangement in front of the eyes of the    spectacles wearer.

Since the above-mentioned disadvantages increasingly occur in spectaclelenses having a flat base curve and a curved back surface, these twoparameters (i.e. base curve and/or curvature of the back surface) canpreferably be taken into consideration by means of an asymptoticprefactor v:k=v*(1−g _(prescription) −h),  (6)where

-   g_(prescription) is a function of at least one prescription value;-   h is a function of at least one parameter of the spectacle lens or    its arrangement in front of the eyes of the spectacles wearer; and-   v is a prefactor, which is a function of the prescription, in    particular of the distance prescription (or the prescription in the    distance reference point), and/or of the base curve of the spectacle    lens and/or of the curvature of the back surface of the spectacle    lens.

For example, the asymptotic prefactor v can be specified such that themanipulation factor k is only applied for minus-power, or negative,lenses.

The prefactor v can be a double asymptote function of the distanceprescription and/or of the base curve of the spectacle lens and/or ofthe curvature of the back surface of the spectacle lens. For example,the prefactor v can be realized by means of a double asymptote functionof the form:

$\begin{matrix}{v = {b + \frac{a}{\left( {1 + {\mathbb{e}}^{{c{({x + d})}}^{m}}} \right)}}} & (7)\end{matrix}$where for x, the medium power or the sphere of the distance prescriptioncan be put. For negative selected c, the value b corresponds to thefactor k, and (b+a)=1.0, so that:

$\begin{matrix}{v = {{b + \frac{a}{\left( {1 + {\mathbb{e}}^{{c{({x + d})}}^{m}}} \right)}} = {k + \frac{1 - k}{\left( {1 + {\mathbb{e}}^{{c{({x + d})}}^{m}}} \right)}}}} & \left( {7a} \right)\end{matrix}$

However, it is conceivable to describe the dependency of the prefactoron the distance portion prescription and/or the base curve and/or thecurvature of the back surface by means of other suitable functions.

Preferably, the function g_(prescription) is a function of theprescription astigmatism and/or of the prescribed cylinder axis and/orof the prescribed addition. The prescription astigmatism, the prescribedcylinder axis, and the prescribed addition are the predetermined valuesthat are determined by means of refraction determination carried out byan optometrist or eye doctor. Accordingly, the method preferablycomprises the step of obtaining the prescription values, in particularthe prescription astigmatism, and/or the prescribed cylinder axis,and/or the prescribed addition.

Preferably, the dependency of the function g_(prescription) on thecylinder axis position is described by the factor (by the function)ƒ_((cylinder axis)):ƒ_((cylinder axis position)) =a*sin³(2*cylinder axis position),  (8)where the parameter a is preferably in the range from 0.05 to 1.0,further preferably in the range from 0.3 to 0.6, and particularlypreferably takes on the value 0.4.

The dependency of the function g_(prescription) on the prescriptionastigmatism is preferably described by the factor (by the function)ƒ_((prescription astigmatism)):

$\begin{matrix}{{f_{({{prescription}\mspace{14mu}{astigmatism}})} = \frac{{prescription}\mspace{14mu}{astigmatism}}{b}},} & (9)\end{matrix}$where the parameter b is preferably in the range from 2 to 6, andfurther preferably in the range from 4 to 6. Particularly preferably, btakes on the value of the maximum prescription astigmatism.

Preferably, the function g_(prescription) is a linear function of theaddition, wherein the dependency of the function g_(prescription) can bedescribed by the factor or by the function ƒ_((addition)):ƒ_((addition)) =c*addition+d,  (10)

The straight line of the addition is preferably selected such that noadjustment takes place for the maximum prescription addition (i.e.ƒ_((addition) _(max) ₎=0) and that with the smallest permissibleaddition ƒ_((addition) _(min) ₎=1.0 applies. Preferably, the straightline parameter c is in the range between 0 and −1, and furtherpreferably in the range between 0.75 and −0.3. Particularly preferably,c takes on a value of −0.3636. Preferably, the parameter d is in therange from 2.0 to 0, further preferably in the range between 2 and 1.Particularly preferably, d takes on the value of 1.2727.

The function g_(prescription) is preferably obtained by multiplying atleast two of the factors or functions ƒ_((cylinder axis)),ƒ_((prescription astigmatism)), and ƒ_((addition)), preferably bymultiplying all three factors.

Preferably, h is a function of the tilt angle of the spectacle lens (h=ƒ_((tilt angle))), preferably a function of the form:

$\begin{matrix}{{f_{({{tilt}\mspace{14mu}{angle}})} = \frac{{tilt}\mspace{14mu}{angle}}{g}},} & (11)\end{matrix}$where g is a predetermined constant. Since the influence of the tiltangle is not very great, g is preferably in the range of 50 to 500,further preferably in the range from 100 to 300, and particularlypreferably the value is approximately 200.

The tilt angle is the angle that is enclosed by the horizontal tangentof the object-side surface of the spectacle lens at a predeterminedreference point and a horizontal straight reference line. Thepredetermined reference point is the intersection of the eye-sidehorizontal main ray in the wearer's zero direction of sight with theobject-side surface of the spectacle lens. The horizontal straightreference line is in a plane perpendicular to the horizontal main ray inthe wearer's zero direction of sight. With regard to the definition andthe determination of the tilt angle, reference is made to DE 10 2004 059448 A1 (referred to as a “horizontaler Kippwinkel”/Engl.: horizontalangle of tilt/). The tilt angle is one of the parameters of thearrangement of the spectacle lens in front of the eyes of the spectacleswearer.

Instead of the tilt angle, h can be a function of the face form angle(FFA), preferably a function of the form:

$\begin{matrix}{h = {f_{({FSW})} = {\frac{FSW}{g}.}}} & (12)\end{matrix}$

Moreover, other individual or average parameters of the wearing positionof the spectacle lens, such as forward inclination, can also be takeninto account.

Preferably, the factor k is calculated depending on the cylinder axisposition, the prescription astigmatism, the addition, and the tilt angleor the face form angle:k=1−ƒ_((cylinder axis position))*ƒ_((prescription astigmatism))*ƒ_((addition))−ƒ_((tilt angle))  (13)ork=v*(1−ƒ_(cylinder axis position)*ƒ_(prescription astigmatism)*ƒ_((addition))−ƒ_((tilt angle))  (14)wherein the individual factors or functions ƒ are each calculatedaccording to equations (8) to (12).

An advantage of a factor k calculated according to formulae (13) or (14)is that the factor k will automatically take on a value of 1 if notransformation of the starting target astigmatism distribution is totake place.

Preferably, the factor k is only applied for prescription cylinder axispositions of 0 to 90° according to TABO with indication in plus cylindernotation for right lenses, for left lenses in the case of cylinder axesof 90 to 180°. With cylinder axis positions in these ranges, theabove-described disadvantages occur increasingly. If the cylinder axispositions are in the other quadrants, the spectacle lens can beoptimized on the basis of the conventional method (e.g. on the basis ofthe method disclosed in DE 10 2008 015 189) thus taking a symmetrictarget astigmatism objectives into account.

After scaling of the temporal astigmatism, the target astigmatism valuescan optionally be scaled or transformed further. For example, theprogression length can depend on the addition by analogy withƒ_((Addition)), as described in DE 10 2008 015 189. The targetastigmatism values can also be scaled depending on the addition, asdescribed in DE 10 2008 015 189, for example. The order of the differentscalings/transformations of the starting target astigmatism distributioncan vary as well.

As explained above, the optimization of the spectacle lens on the basisof the transformed target astigmatism distribution can comprise aminimization of a target function in which the values of the previouslydetermined transformed target astigmatism distribution are taken intoaccount as target values. Preferably, the optimization of the spectaclelens on the basis of the transformed target astigmatism distributioncomprises a minimization of a target function of the form:

$\begin{matrix}{{{F\left( \overset{->}{x} \right)} = {\sum\limits_{i = 1}^{m}\left\lbrack {{g_{i,{Ast}}\left( {{Ast}_{i} - {Ast}_{i,{target}_{new}}} \right)}^{2} + \ldots} \right\rbrack}},} & (15)\end{matrix}$where

-   Ast_(i,target) _(new) is the target astigmatism value of the    transformed target astigmatism distribution Ast_(target) _(new) at    the i^(th) evaluation point;-   Ast_(i) is the actual local astigmatism at the i^(th) evaluation    point; and-   g_(i,Ast) is the local weighting of the target astigmatism value at    the i^(th) evaluation point

In the above formula, Ast_(i,target) _(new) is the previouslydetermined, transformed target astigmatism distribution Ast_(target)_(new) at the i^(th) evaluation point.

Further preferably, the refractive error/refractive power ΔR is alsotaken into account in the target function, so that calculating andoptimizing the spectacle lens comprises minimizing the target function:

$\begin{matrix}{{F\left( \overset{->}{x} \right)} = {\sum\limits_{i = 1}^{m}\left\lbrack {{g_{i,{\Delta\; R}}\left( {{\Delta\; R_{i}} - {\Delta\; R_{i,{target}_{new}}}} \right)}^{2} + {g_{i,{Ast}}\left( {{Ast}_{i} - {Ast}_{i,{target}_{new}}} \right)}^{2} + \ldots} \right\rbrack}} & (16)\end{matrix}$where

-   ΔR_(i,target) _(new) is the target value of the local refractive    error/refractive power at the i^(th) evaluation point;-   ΔR_(i) is the actual value of the local refractive error/refractive    power at the i^(th) evaluation point; and-   g_(i,ΔR) is the local weighting of the refractive error/refractive    power at the i^(th) evaluation point.

Similar to the target astigmatism distribution, the distribution of thetarget refractive power or of the target refractive error can bedetermined from a starting target astigmatism distribution or a startingtarget refractive error distribution and be modified by multiplicationby a factor. The distribution of the target refractive power or of thetarget refractive error can also be determined on the basis of thepreviously determined modified target astigmatism distribution.

The optimization of the spectacle lens is preferably performed in thewearing position of the spectacle lens. In the optimization process ofthe spectacle lens, in addition to the individual prescription values(sph, cyl, axis, add, prism, base), parameters of the individualposition or arrangement of the spectacle lens in front of the spectacleswearer's eye (e.g. corneal vertex distance (CVD), face form angle (FFA),forward inclination or pantoscopic angle), and/or physiologicalparameters of the spectacles wearer (e.g. pupillary distance) arepreferably taken into account as well. Alternatively, average parametersof the position or arrangement of the spectacle lens in front of the eyeof the spectacles wearer and/or average physiological parameters of thespectacles wearer can be taken into account. The progressive spectaclelens can be optimized and calculated “online” as one-of-a-kind afterreceipt of order.

Preferably, the method comprises the further steps of:

-   -   obtaining the prescription values of the spectacle lens; and    -   obtaining the preferably individual parameters of the spectacle        lens and/or the arrangement of the spectacle lens in front of        the eyes of the spectacles wearer.

With the above-described procedure according to the first aspect of theinvention, it is possible to manipulate the target astigmatismdistribution required for the optimization on the basis of targetfunctions for specific powers in an existing progressive spectacle lensdesign (starting design, base design) such that the objectives can beachieved more easily. Thus, the negative effects on the optimizedsurface and wearing position properties of disadvantageous target valueobjectives can be reduced clearly. This directly improves the wearingposition properties.

The method and the corresponding device according to the first aspect ofthe invention are suitable both for creating designs and design variantsfor conventional or power-optimized progressive spectacle lenses and forcreating designs and design variants for individually optimizedprogressive spectacle lenses.

As explained above, the optimization of progressive spectacle lenses isusually performed by minimizing a target function in which required ortarget values for at least one optical parameter (e.g. astigmatismand/or refractive power) or required or target values for at least oneaberration (e.g. astigmatic error or astigmatic deviation and/orrefractive error) of the progressive spectacle lens are taken intoaccount. The required or target values of the at least one opticalproperty or the at least one aberration, which are taken into account inthe target function, characterize the design of a spectacle lens. Inaddition, the spectacle lens design can comprise a suitable objectdistance model. The object distance model may comprise an objectdistance function, which is defined as the reciprocal object distancealong the main line of sight. A standardized object distance model isindicated in DIN 58 208 part 2 (cf. image 6), for example. However, theobject distance model may be different from this standardized objectdistance model.

A main line of sight is understood to be the sequence of the penetrationpoints of the main rays through the respective spectacle lens surfacewhen looking at a line lying in the perpendicular plane that splits thedistance of the two ocular centers of rotation in half (so-calledcyclopean eye plane). The spectacle lens surface can be the object-sideor the eye-side surface. The position of the line in the cyclopean eyeplane is determined by the selected object distance model.

A main line is understood to be a substantially straight or curved linealong which the desired increase of the refractive power of thespectacle lens from the distance portion to the near portion isachieved. The main line is substantially centered with respect to thespectacle lens top down, i.e. along a substantially vertical direction.Thus, the main line constitutes a construction line in the coordinatesystem of the object-side or eye-side surface to be optimized for thedescription of the target values. The course of the main line of thespectacle lens is selected such that it at least approximately followsthe main line of sight. A method for adjusting the main line to the mainline of sight is described in EP 1 277 079 A2, for example.

The object distance function (i.e. the reciprocal object distance on themain line of sight) plays an essential role in the design specificationand optimization of progressive spectacle lenses. For example, accordingto the Minkwitz theorem, in the case of a fullcorrection to the greatestpossible extent, the basic characteristic of a progressive spectaclelens in the surrounding of the main line of sight is mainly determinedby the course of the object distance function A₁(y) along the main lineof sight.

It is a further object of the invention to provide an efficient andquick method for an automatic adjustment of the object distance functionto changed object distances or to a modified object distance model.

According to a second aspect of the invention, a computer-implementedmethod for optimizing a progressive spectacle lens is proposed, themethod comprising the steps of:

-   -   specifying a starting object distance function A_(1G)(y)    -   obtaining object distance data, wherein the object distance data        comprises an object distance in at least one predetermined point        on the main line of sight;    -   modifying or transforming the starting object distance function        depending on the obtained object distance data; and    -   optimizing the progressive spectacle lens, wherein in the        optimization process of the spectacle lens the        modified/transformed object distance function is taken into        account.

Modifying/Transforming the starting object distance function A_(1G)(y)comprises overlaying the starting object distance function A_(1G)(y)with a correction function A_(1corr)(y):A ₁(y)=A _(1G)(y)+A _(1corr)(y).  (17)

The object distance function represents the reciprocal object distance(the reciprocal object separation) along the main line of sight as afunction of the vertical coordinate y. Put differently, the objectdistance function is defined as the reciprocal object distance (thereciprocal object separation) along the main line of sight.

The correction function includes at least one variable parameter, whichis determined depending on the obtained object distance data such thatthe value of the modified starting object distance function, in at leastone predetermined point, is equal to the reciprocal value of theobtained target object distance for this point. In other words, the atleast one variable parameter (coefficient) of the correction function isdetermined or set depending on the obtained object distance data suchthat the conditionA ₁(y=y _(D))=A _(1D),  (18)is met, wherein in the above formula:

-   A_(1D) is the reciprocal value of the obtained target object    distance or the obtained target object separation in the at least    one predetermined point D on the main line of sight, wherein the    point D has a vertical coordinate y_(D); and-   A₁(y=y_(D)) is the value of the object distance function A₁(y) in    the predetermined point D on the main line of sight.

Here, the coordinate system can be an arbitrary coordinate system, inparticular one of the above-described coordinate systems {x,y} or {u,y},where u designates the distance from the main line of sight or mainline. In a coordinate system {x,y}, (x=x_(HBL)=x₀,y) applies for thepoints on the main line of sight (HBL). In a coordinate system {u,y} ofthe main line of sight, (u=0,y) applies for the points on the main lineof sight.

Preferably, the object distance data comprises at least one targetobject distance A_(1distance) in a predetermined distance referencepoint (design point distance) DF on the main line of sight and a targetobject distance A_(1near) in a predetermined near reference point(design point near) DN on the main line of sight. The at least onevariable parameter of the correction function is determined or set suchthat the respective value of the modified starting object distancefunction in the distance and/or near reference point(s) is equal to thecorresponding reciprocal value of the detected target object distancefor the distance and/or near reference point(s).

Put differently, in this case, the object distance data comprises atarget object distance for the distance reference point DF and a targetobject distance for the near reference point DN. The distance referencepoint is located on the main line of sight at a vertical height y_(DF).The near reference point is located on the main line of sight at avertical height y_(DN). The at least one variable parameter of thecorrection function is set such that the conditionsA ₁(y=y _(DF))=A _(1distance),A ₁(y=y _(DN))=A _(1near)   (19)are met, where

-   A_(1distance) is the reciprocal value of the target object distance    in the distance reference point DF, and-   A_(1near) is the reciprocal value of the target object distance in    the near reference point DN.

The starting object distance function, hereinafter referred to as abasic object distance function or basic function,A_(1G)(y)=A_(1G)(x=x₀,y)=A_(1G)(u=0,y) can be an arbitrary analyticalfunction or also an interpolation function (e.g. spline function). Also,A_(1G)(y) can be specified point by point.

For example, the starting object distance function can be describedanalytically by means of a double asymptote function of the form:

$\begin{matrix}{{A_{1\; G}(y)} = {{{DAS}_{G}(y)} = {b_{G} + \frac{a_{G}}{\left( {1 + {\mathbb{e}}^{c{({y + d})}}} \right)^{m}}}}} & (20)\end{matrix}$with the parameters/variables a_(G),b_(G),c,d,m.

Particularly, a double asymptote function has the following advantageousproperties:

-   -   The two asymptotes respectively take on the values b_(G) and        (b_(G)+a_(G));    -   The vertical position can be controlled with the variable        parameter d. Preferably, the parameter d is in the range of        −10<d<10, further preferably in the range of −8<d<5;    -   The larger the value of the variable parameter c, the faster the        transition from asymptote to the other. The parameter c is        preferably selected such that |c|<1.5;    -   The parameter m (m>0) describes the asymmetry of the function.        For m=1, the double asymptote function has a point symmetry with        a center y=−d. Preferably, the parameter m is in the range of        0.2<m<2, further preferably in the range of 0.4<m<1;    -   If the negative sign (c<0) is selected for the parameter c, it        will hold that:        -   near portion asymptote A_(1G)(y→−∞)=A_(1Gnear)=b_(G); and        -   distance portion asymptote            A_(1G)(y→+∞)=A_(1distance)=(b_(G)+a_(G)).

Usually, the starting object distance function A_(1G)(y), which isassigned to the starting design (base design), is specified such thatthe object distances in the distance reference point DF and in the nearreference point DN (design points distance and near) approximatelycorrespond to the standard object distances A_(1Gdistance) andA_(1Gnear) i.e. the target object distances in the distance and nearreference points according to a standard object distance model.Consequently, the parameters a_(G),b_(G) can be determined automaticallyon the basis of the standard objectives for the reciprocal objectdistances A_(1Gdistance) and A_(1Gnear) in the distance and nearreference points DF and DN. A standard object distance model is e.g.indicated in DIN 58 208 part 2.

If a spectacles wearer selects deviating object distances A_(1distance)and A_(1near) in the distance and/or near reference point(s), thestarting object distance function will be overlaid with a correctionfunction in order to take this modification into account.

The correction function A_(1corr)(y) may be

-   -   a double asymptote function of the form

${A_{corr}(y)} = {{{DAS}_{corr}(y)} = {b_{corr} + \frac{a_{corr}}{\left( {1 + {\mathbb{e}}^{c_{corr}{({y + d_{corr}})}}} \right)^{m_{corr}}}}}$

-   -    with the parameters (coefficients) a_(corr), b_(corr),        c_(corr), d_(corr),m_(corr);    -   a linear function of the starting object distance function        A_(1corr)(y)=c+mA_(1G)(y) with the parameters (coefficients) c        and m; or    -   a different suitable function.

Alternatively or in addition, the starting object distance function canbe overlaid with other functions to e.g. obtain a desired modificationof the design characteristics. For example, the starting object distancefunction can be overlaid with a function in the form of a Gaussian bellcurve

${A_{1\;{corr}}(y)} = {{A_{1\;{Gauss}}(y)} = {{g(y)} = {g_{a} + {g_{b}{\mathbb{e}}^{- \frac{y - y_{0}}{\sigma}}}}}}$with the parameters (coefficients) g_(a),g_(b),y₀,σ.

At least one of the parameters of the correction function is variableand is determined or set depending on the obtained object distance data,in particular on the modified target values for the object distances inthe distance and/or near reference point(s).

Preferably, the correction function is a double asymptote function ofthe form

$\begin{matrix}{{A_{corr}(y)} = {{{DAS}_{corr}(y)} = {b_{corr} + \frac{a_{corr}}{\left( {1 + {\mathbb{e}}^{c_{corr}{({y + d_{corr}})}}} \right)^{m_{corr}}}}}} & (21)\end{matrix}$with the parameters (coefficients)a_(corr),b_(corr),c_(corr),d_(corr),m_(corr).

In this case, it holds that:A ₁(y)=A _(1G)(y)+DAS _(corr)(y)  (22)

The variable parameters/coefficients b_(corr) and a_(corr) of thecorrection function are determined or set depending on the obtainedobject distance data.

Preferably, both the starting object distance function and thecorrection function are double asymptote functions. Preferably, thecorrection function has the same parameters c, d and m as the parametersof the starting object distance function (i.e.c=c_(corr),d=d_(corr),m=m_(corr)). In this case, it holds that:

$\begin{matrix}{{A_{1}(y)} = {{{A_{1\; G}(y)} + {{DAS}_{corr}(y)}} = {{\left( {b_{G} + \frac{a_{G}}{\left( {1 + {\mathbb{e}}^{c{({y + d})}}} \right)^{m}}} \right) + \left( {b_{cor} + \frac{a_{corr}}{\left( {1 + {\mathbb{e}}^{c{({y + d})}}} \right)^{m}}} \right)} = {\left( {b_{G} + b_{corr}} \right) + {\frac{\left( {a_{G} + a_{corr}} \right)}{\left( {1 + {\mathbb{e}}^{c{({y + d})}}} \right)^{m}}.}}}}} & (23)\end{matrix}$

Thus, it can be ensured that the characteristic of the starting objectdistance function is substantially maintained in the case of anadjustment to changed object distances.

With the two conditions A₁(y_(D) _(F) )=A_(1distance) and A₁(y_(D) _(N))=A_(1near), the two coefficients b=(b_(G)+b_(corr)) anda=(a_(G)+a_(corr)) and thus also the coefficients b_(corr)=(b−b_(G)) anda_(corr)=(a−a_(G)) of the correction function are clearly determined.

The coefficients/parameters of the starting object distance function(basic function) and the coefficients/parameters of the correctionfunction can be determined in advance and preferably be storedseparately as data files in a memory. This allows a simple reproductionand modification of the values of the starting design later on.

As explained above, the starting object distance function, which may inparticular be a double asymptote function, can alternatively or inaddition to an overlay with a correction function A_(1corr)(y) beoverlaid with a function in the form of a Gaussian bell curve

${A_{1{Gauss}}(y)} = {{g(y)} = {g_{a} + {g_{b}{\mathbb{e}}^{- \frac{y - y_{0}}{\sigma}}}}}$with the parameters/coefficients g_(a),g_(b),y₀,σ:

$\begin{matrix}{{A_{1}(y)} = {{{A_{1G}(y)} + {A_{1\;{Gauss}}(y)}} = {{A_{1G}(y)} + {\left( {g_{a} + {g_{b}{\mathbb{e}}^{- \frac{y - y_{0}}{\sigma}}}} \right).}}}} & (24)\end{matrix}$

In case that the starting object distance function is a double asymptotefunction, it holds that:

$\begin{matrix}{{A_{1}(y)} = {{{A_{1G}(y)} + {A_{1\;{Gauss}}(y)}} = {\left( {b\;\frac{a}{\left( {1 + {\mathbb{e}}^{c{({y + d})}}} \right)^{m}}} \right) + {\left( {g_{a} + {g_{b}{\mathbb{e}}^{- \frac{y - y_{0}}{\sigma}}}} \right).}}}} & (25)\end{matrix}$

Due to the starting object distance function (basic function) beingoverlaid with a Gaussian bell curve (Gaussian function), the curvecharacteristic of the starting object distance function can be modifiedin a targeted manner. In particular, the Gaussian function has theeffect that the object distance function is flatter above the Gaussianmaximum. The refractive power change becomes less in this zone, theisoastigmatism lines move further outward, and the substantiallydeficit-free lens zone, e.g. the lens zone having an astigmatic error ofsmaller than 0.5 dpt, becomes wider. Thus, zones (e.g. the intermediatezone) can be given a higher or lower weighting in a targeted manner.

For example, from a uniform slow transition from the distance portionvalue of the object distance A_(1Gdistance) to the near portion value ofthe object distance A_(1Gnear) (g_(b)≈0), a different course of theobject distance function A₁(u=0,y)=A₁(y) (A₁−course) can be created fora lens for computer work (g_(b)≠0, σ≠0).

In one example, on the basis of a percentage weighting g_(G) of theGaussian function, where g_(G)ε[0,100]%, the associated coefficientg_(b) of the Gaussian function can be determined according to thespecification of a maximum A₁-increase of the Gaussian functiong_(b max) (a design-specific specification):

$\begin{matrix}{g_{b} = {\frac{g_{G}}{100}{g_{b\;\max}.}}} & (26)\end{matrix}$

With a 90% weighting of the Gaussian function and a maximum A₁-increaseof the Gaussian function g_(b max)=0.6 dpt, a value of e.g. 0.54 dptresults for g_(b).

The percentage weighting g_(G) and the further coefficients of theGaussian function can be specified for the respective base design or canbe determined according to the method described WO 2010/084019 on thebasis of a design polygon. Preferably, the parameter g_(a) is in therange of −1<g_(a)<1, further preferably g_(a)=0. The parameter y₀ ispreferably in the range of −10<y₀<5, further preferably in the range of−5<y₀<0. The parameter σ is preferably in the range of 0<σ<15, furtherpreferably in the range of 5<σ<10.

Overlaying the starting object distance function with a Gaussian bellcurve can be independent of an overlay with a correction function,according to a further aspect.

According to a further example, the correction function A_(corr)(y) is alinear function of the starting object distance function:A _(corr)(y)=c+mA _(1G)(y)  (27)with the parameters/coefficients c and m.

Thus, the modified object distance function also represents a linearfunction of the starting object distance functionA_(1G)(u=0,y)=A_(1G)(y):A ₁(y)=A _(1G)(y)+c+mA _(1G)(y)=c+(1+m)A _(1G)(y)  (28)or in a short notationA ₁ =A _(1G) +c+mA _(1G) =c+(1+m)A _(1G).  (29)

Preferably, the straight line coefficients c and m are calculated fromthe deviations of the values of the starting object distance functionA_(1G)(y) from the obtained target values of the reciprocal objectdistance in the distance and near reference points. Put differently, alinear adjustment of the starting object distance function to thechanged object distances in the distance and/or or near referencepoint(s) is performed.

Preferably, in this case, it holds for the coefficients c and m that:

$\begin{matrix}{{c = \frac{{\Delta\; A_{1\; F}{A_{1\; G}\left( y_{DN} \right)}} - {\Delta\; A_{1N}{A_{1\; G}\left( y_{DF} \right)}}}{{A_{1\; G}\left( y_{DN} \right)} - {A_{1G}\left( y_{DF} \right)}}}{{m = \frac{{\Delta\; A_{1\; N}} - {\Delta\; A_{1\; F}}}{{A_{1\; G}\left( y_{DN} \right)} - {A_{1\; G}\left( y_{DF} \right)}}},}} & (30)\end{matrix}$where

-   ΔA_(1F)=A_(1distance)−A_(1G)(y_(DF));-   ΔA_(1N)=A_(1near)−A_(1G)(y_(DN));-   A_(1distance) is the reciprocal value of the target object distance    in the distance reference point;-   A_(1near) is the reciprocal value of the target object distance in    the near reference point; near;-   y_(F) is the vertical coordinate of the distance reference point;    and-   y_(N) is the vertical coordinate of the near reference point.

The straight line coefficients c and m are calculated as follows, forexample:

In a first step, the deviations of the values of the starting objectdistance function A_(1G)(y) in the reference or design points DF (withthe coordinates (x=x₀,y_(DF))=(u=0,y_(DF))) and DN (with the coordinates(x=x₀,y_(DN))=(u=0,y_(DN))) from the corresponding (individual) valuesA_(1distance) and A_(1near) of the reciprocal target object distance(the reciprocal target object separation) are determined for thesepoints:ΔA _(1F) =A _(1distance) −A _(1G)(y _(DF));ΔA _(1N) =A _(1near) −A _(1G)(y _(DN));  (31)

The straight line coefficients c and m can be calculated from thepreviously determined deviations as follows:

$\begin{matrix}{c = \frac{{\Delta\; A_{1F}{A_{1G}\left( y_{DN} \right)}} - {\Delta\; A_{1N}{A_{1G}\left( y_{DF} \right)}}}{{A_{1G}\left( y_{DN} \right)} - {A_{1G}\left( y_{DF} \right)}}} & (32) \\{m = \frac{{\Delta\; A_{1N}} - {\Delta\; A_{1F}}}{{A_{1G}\left( y_{DN} \right)} - {A_{1G}\left( y_{DF} \right)}}} & (32)\end{matrix}$

In the above formulae:

-   A_(1G)(y) is the starting object distance function;-   A_(1distance) is the target value of the reciprocal object distance    in the distance reference point (design point distance);-   A_(1near) is the target value of the reciprocal object distance in    the near reference point (design point near); and-   A₁(y) is the corrected/adjusted object distance function.

By this adjusted object distance function, which is a linear function ofthe starting object distance function, the course of the reciprocalobject distance along the main line of sight is not changedsubstantially. In particular, the slope or derivative of the basicfunction A_(1G)(y) and of the modified/corrected object distancefunction A₁(y) merely differ by the constant factor (1+m):

$\begin{matrix}{\frac{\mathbb{d}A_{1}}{\mathbb{d}y} = {{\frac{\mathbb{d}A_{1G}}{\mathbb{d}y} + {m\frac{\mathbb{d}A_{1G}}{\mathbb{d}y}}} = {\frac{\mathbb{d}A_{1G}}{\mathbb{d}y}\left( {1 + m} \right)}}} & (33)\end{matrix}$

Put differently, the first derivative of the starting object distancefunction is only changed by a factor (1+m). For example, in the case ofa fullcorrection to the greatest possible extent, the basiccharacteristic of a progressive spectacle lens in the surrounding of themain line of sight is mainly determined by the course of the objectdistance function A₁(y) along the main line of sight (Minkwitz theorem).The linear adjustment of the starting object distance function makes itpossible to maintain the design characteristic with negligible computingeffort also in the case of an adjustment of the object distances tomodified specifications in one or two points.

The above-described method can be applied irrespective of the course ofthe reciprocal object distance along the main line of sight. It is alsopossible to substantially maintain the characteristic of the objectdistance function along the main line of sight and at the same time varythe object distances in the design points/reference points depending onthe design, or to adjust them to the needs and wishes of the spectacleswearer.

In this example, the starting object distance function (basic function)A_(1G)(y) can be an arbitrary analytical function or also aninterpolation function (e.g. spline function). Coefficients of the basicfunction do not have to be known or be changed. If A_(1G)(y) isspecified point by point or, as described in the patent application DE10 2009 005 847.8, is changed before the optimization, this method willbe particularly suitable for matching the object distance function tothe individual target object distances in the design points or referencepoints.

The above-described transformations of the starting object distancefunction by overlaying the starting object distance function with adouble asymptote correction function, by overlaying the starting objectdistance function with a Gaussian function, or by a linear adjustmentcan of course be combined with each other in an arbitrary order.

As explained above, the optimization of the spectacle lens on the basisof the transformed target astigmatism distribution can comprise aminimization of a target function in which target values for the targetastigmatism and/or for the refractive error are taken into account (cf.equations (1) and (2) or equations (15) and (16)). The values taken intoaccount in the target function can be the values of an asymmetric targetastigmatism distribution (Ast_(target) _(new) ) determined according toa preferred example of the invention. The target astigmatismdistribution can also be an arbitrary, predetermined target astigmatismdistribution, e.g. a target astigmatism distribution determined by meansof the method disclosed in DE 10 2008 015 189, DE 10 2009 005 206, or DE10 2009 005 214. The refractive power distribution of the spectaclelens, the target values of which are taken into account in the targetfunction, is preferably a refractive power distribution that isdetermined taking a predetermined accommodation model of the eye of thespectacles wearer and the previously determined object distance functioninto consideration. The target refractive power distribution can e.g. bedetermined such that a substantially full correction (i.e. within thescope of tolerable residual errors) along the main line of sight ispresent with the spectacle lens. Put differently, the objects which arelooked at during an eye movement along the main line of sight and theobject distance of which is determined by the object distance functionare optimally imaged in the eye's fovea.

Preferably, the spectacle lens is optimized in the wearing position ofthe spectacle lens. In the optimization process of the spectacle lens,in addition to the individual prescription values (sph, cyl, axis, add,prism, base), parameters of the individual position or arrangement ofthe spectacle lens in front of the spectacles wearer's eye (e.g. cornealvertex distance (CVD), face form angle (FFA), forward inclination orpantoscopic angle), and/or physiological parameters of the spectacleswearer (e.g. pupillary distance) are preferably taken into account aswell. Alternatively, average parameters of the position or arrangementof the spectacle lens in front of the eye of the spectacles wearerand/or average physiological parameters of the spectacles wearer can betaken into account. The progressive spectacle lens can be optimized andcalculated online as one-of-a-kind after receipt of order.

Preferably, the method comprises the further steps of:

-   -   obtaining the prescription values of the spectacle lens; and    -   obtaining the preferably individual parameters of the spectacle        lens and/or the arrangement of the spectacle lens in front of        the eyes of the spectacles wearer.

According to the invention, a computer program product, i.e. a computerprogram claimed in the patent category of a device, and a storage mediumwith a computer program stored thereon are provided, wherein thecomputer program is adapted, when loaded and executed on a computer, toperform a preferred method for optimizing a progressive spectacle lensaccording to the first or second aspects of the invention.

Moreover, according to one aspect, a device for optimizing a progressivespectacle lens is proposed, comprising optimizing means adapted toperform a calculation or optimization of the spectacle lens according toa preferred example of the method for optimizing a progressive spectaclelens according to the first and/or second aspect(s) of the invention.

Specifically, the device for optimizing a progressive spectacle lenscomprises

-   -   storage means for storing a starting target astigmatism        distribution Ast_(target) _(start) for the progressive spectacle        lens;    -   target astigmatism distribution calculating means adapted to        determine a transformed target astigmatism distribution        Ast_(target) _(new) from the starting target astigmatism        distribution; and    -   spectacle lens optimizing means adapted to optimize a        progressive spectacle lens on the basis of the transformed        target astigmatism distribution.

The target astigmatism distribution calculating means are adapted toperform

-   -   a multiplication of the value of the maximum temporal target        astigmatism max_Ast_(target—)temporal_(start) of the starting        target astigmatism distribution Ast_(target) _(start) by a        factor k:    -   max_(—) Ast _(target—)temporal_(new) =k*max_(—) Ast        _(target—)temporal_(start),    -   whereby a modified maximum temporal astigmatism        max_Ast_(target—)temporal_(new) results, wherein the factor k is        a function of at least one prescription value and/or of at least        one parameter of the spectacle lens or its arrangement in front        of the eyes of the spectacles wearer; and    -   a transformation of the starting target astigmatism distribution        Ast_(target) _(start) on the basis of the modified maximum        temporal astigmatism max_Ast_(target) temporal_(new).

The starting target astigmatism distribution Ast_(target) _(start) canbe stored in a memory permanently or temporarily. The target astigmatismdistribution calculating means and the spectacle lens optimizing meanscan be implemented by means of correspondingly configured or programmedconventional computer, specialized hardware and/or computer networks orcomputer systems. It is possible for the same computer or the samecomputer system to be configured or programmed so as to perform both thecalculation of a transformed target astigmatism distribution and theoptimization of the spectacle lens on the basis of the transformedtarget astigmatism distribution. However, it is of course possible toperform the calculation of the transformed target astigmatismdistribution and the calculation of the spectacle lens on the basis ofthe transformed target astigmatism distribution in separate computingunits, for example in separate computer or computer systems.

The target astigmatism distribution calculating means and/or thespectacle lens optimizing means can be in signal communication with thememory by means of suitable interfaces, and in particular read outand/or modify the data stored in the memory. Moreover, the targetastigmatism distribution calculating means and/or the spectacle lensoptimizing means can preferably comprise an interactive graphical userinterface (GUI), which allows a wearer to visualize the calculation ofthe transformed target astigmatism distribution Ast_(target) _(new) andthe optimization of the progressive spectacle lens and to control itoptionally by changing one or more parameters.

Alternatively or in addition, the device for optimizing a progressivespectacle lens can comprise

-   -   object distance function specifying means adapted to specify or        set a starting object distance function A_(1G)(y),    -   object distance obtaining means adapted to obtain object        distance data, wherein the object distance data comprises an        object distance in at least one predetermined point on the main        line of sight;    -   object distance function modifying means for modifying or        transforming the starting object distance function depending on        the obtained object distance data; and    -   spectacle lens optimizing means for optimizing the progressive        spectacle lens, wherein in the optimization process of the        spectacle lens the transformed object distance function is taken        into account.

The object distance function represents the reciprocal object distanceor the reciprocal object separation along the main line of sight as afunction of the vertical coordinate y.

Modifying or transforming the starting object distance functionA_(1G)(y) comprises overlaying A₁(y)=A_(1G)(y)+_(1corr)(y) of thestarting object distance function A_(1G)(y) with a correction functionA_(1corr)(y). The correction function includes at least one variableparameter, which is determined depending on the obtained object distancedata such that the value of the modified starting object distancefunction, in at least one predetermined point, is equal to thereciprocal value of the obtained target object distance for this point.

The object distance function specifying means can comprise storage meansin which the starting object distance function or the parameters of thestarting object distance function, on the basis of which the startingobject distance function can be reconstructed, can be stored permanentlyor temporarily. The object distance obtaining means can comprise atleast one interactive graphical user interface (GUI), which allows awearer to input and/or modify data concerning the desired objectdistances in at least one predetermined point.

The object distance function modifying means and the spectacle lensoptimizing means can be implemented by means of correspondinglyconfigured or programmed conventional computer, specialized hardwareand/or computer networks or computer systems. It is possible for thesame computer or the same computer system, which performs thecalculation of a transformed object distance function (and optionally atransformed target astigmatism distribution) to be capable of performingalso the optimization of the spectacle lens on the basis of thetransformed object distance function. However, it is of course possibleto perform the calculation of the transformed object distance functionand the calculation of the spectacle lens on the basis of thetransformed object distance function in separate computing units, forexample in separate computer or computer systems.

The object distance function modifying means and the spectacle lensoptimizing means can be in signal communication with each other by meansof suitable interfaces.

The object distance function modifying means can also be in signalcommunication with the object distance function specifying means bymeans of suitable interfaces and in particular read out and/or modifythe data stored in the storage means.

Further, the object distance function modifying means and/or thespectacle lens optimizing means can preferably each comprise interactivegraphical user interfaces (GUI), which allow a wearer to visualize thecalculation of the transformed object distance function and theoptimization of the progressive spectacle lens and to control itoptionally by changing one or more parameters.

According to a further aspect, a method for producing a progressivespectacle lens is proposed, comprising:

-   -   optimizing the spectacle lens according to a preferred example        of the method for optimizing a progressive spectacle lens        according to the first and/or second aspect(s) of the invention,    -   providing surface data of the calculated and optimized spectacle        lens; and    -   manufacturing the spectacle lens according to the provided        surface data of the spectacle lens.

The spectacle lens can be manufactured or processed by means of CNCmachines, by means of a casting process, a combination of the twoprocesses, or according to a different suitable process.

Also, a device for producing a progressive spectacle lens is provided,comprising:

-   -   optimizing means adapted to perform a calculation and        optimization of the spectacle lens according to a preferred        example of the method for optimizing a progressive spectacle        lens; and    -   processing means for finishing the spectacle lens.

The optimizing means can be the above-described device for optimizing aprogressive spectacle lens.

As explained above, the processing means can e.g. comprise CNC machinesfor direct machining of a blank according to the determined optimizationobjectives. The finished spectacle lens can have a simple spherical orrotationally symmetric aspherical surface and a progressive surface,wherein the progressive surface is optimized taking an individual objectdistance function and/or a (asymmetric) target astigmatism distributionas well as, optionally, individual parameters of the spectacles wearerinto account. Preferably, the spherical or rotationally symmetricaspherical surface is the front surface (i.e. the object-side surface)of the spectacle lens. Of course, it is also possible to arrange thesurface optimized on the basis of the calculated design as the frontsurface of the spectacle lens. It is also possible that both surfaces ofthe spectacle lens are progressive surfaces. Further, it is possible tooptimize both surfaces of the spectacle lens.

The device for producing a progressive spectacle lens can furthercomprise obtaining means for

-   -   obtaining the prescription values of the spectacle lens; and    -   obtaining the (individual) parameters of the spectacle lens        and/or of the arrangement of the spectacle lens in front of the        eyes of the spectacles wearer.

Alternatively or in addition, the device for producing a progressivespectacle lens can further comprise obtaining means for obtaining objectdistance data. The obtaining means can in particular comprise graphicaluser interfaces.

Moreover, there is proposed a progressive spectacle lens producedaccording to a preferred production method, as well as a use of aprogressive spectacle lens, produced according to a preferred productionmethod, in a predetermined average or individual wearing position of thespectacle lens in front of the eyes of a specific spectacles wearer, forcorrecting a visual defect of the spectacles wearer.

With the proposed procedure for modifying the object distance functionaccording to a preferred example, it is possible to adjust apredetermined starting object distance function, which e.g. correspondsto a standard object distance model, quickly and with comparativelylittle computing effort to a model for the object distances (objectseparations), which is different from the standard object distancemodel. Moreover, it is possible to change the characteristics of thestarting object distance function in a targeted manner and to thuscreate object distance functions for different spectacle lens designs.

BRIEF DESCRIPTION OF THE DRAWINGS

Further objects, features, and advantages of the present invention willbecome apparent from the following detailed description of exemplary andpreferred embodiments of the present invention with reference to thedrawings, which show:

FIG. 1 starting target astigmatism distribution for an addition of 2.5dpt;

FIG. 2 target astigmatism distribution for an addition of 2.5 dpt with ascaling of the temporal astigmatism;

FIG. 3 the scaled target astigmatism distribution shown in FIG. 2, whichis additionally scaled depending on the addition;

FIG. 4 the starting target astigmatism distribution scaled depending onthe addition;

FIG. 5 a portion of a graphical user interface for setting the prefactorv;

FIG. 6A an example of a starting target astigmatism distribution;

FIG. 6B an example of a modified/transformed target astigmatismdistribution calculated from the starting target astigmatismdistribution shown in FIG. 6A;

FIG. 7A the surface power of the progressive surface of a progressivespectacle lens optimized on the basis of the starting target astigmatismdistribution shown in FIG. 6A;

FIG. 7B the surface power of the progressive surface of a progressivespectacle lens optimized on the basis of the transformed targetastigmatism distribution shown in FIG. 6B;

FIG. 8A the gradient of the surface power of the progressive surface ofthe progressive spectacle lens optimized on the basis of the startingtarget astigmatism distribution shown in FIG. 6A;

FIG. 8B the gradient of the surface power of the progressive surface ofthe progressive spectacle lens optimized on the basis of the transformedtarget astigmatism distribution shown in FIG. 6B;

FIG. 9A the surface astigmatism of the progressive surface of theprogressive spectacle lens optimized on the basis of the starting targetastigmatism distribution shown in FIG. 6A;

FIG. 9B the surface astigmatism of the progressive surface of theprogressive spectacle lens optimized on the basis of the transformedtarget astigmatism distribution shown in FIG. 6B;

FIG. 10A the gradient of the surface astigmatism of the progressivesurface of the progressive spectacle lens optimized on the basis of thestarting target astigmatism distribution shown in FIG. 6A;

FIG. 10B the gradient of the surface astigmatism of the progressivesurface of the progressive spectacle lens optimized on the basis of thetransformed target astigmatism distribution shown in FIG. 6B;

FIG. 11A the astigmatism in the wearing position of the progressivespectacle lens optimized on the basis of the starting target astigmatismdistribution shown in FIG. 6A;

FIG. 11B the astigmatism in the wearing position of the progressivespectacle lens optimized on the basis of the transformed targetastigmatism distribution shown in FIG. 6B;

FIG. 12A the mean refractive power in the wearing position of theprogressive spectacle lens optimized on the basis of the starting targetastigmatism distribution shown in FIG. 6A;

FIG. 12B the mean refractive power in the wearing position of theprogressive spectacle lens optimized on the basis of the transformedtarget astigmatism distribution shown in FIG. 6B;

FIGS. 13A,B the image formation of objects at different object distancesthrough a spectacle lens;

FIGS. 14A,B the reciprocal object distance (in dpt) along the main lineof sight according to an example of the invention;

FIGS. 15A-15H an example of an adjustment of a starting object distancefunction to a modified object distance model, wherein

FIG. 15A is a further exemplary starting object distance function;

FIG. 15B is the slope of the starting object distance function;

FIG. 15C is an exemplary Gaussian function;

FIG. 15D is the slope of the Gaussian function;

FIG. 15E is the object distance function obtained by overlaying thestarting object distance function with the Gaussian function;

FIG. 15F is the slope of the object distance function;

FIG. 15G is the object distance function modified by linear adjustment;and

FIG. 15H is the slope of the object distance function modified by linearadjustment;

FIGS. 16A-16C an example of a graphical user interface for visualizingand modifying the object distance function, wherein

FIG. 16A is a portion for visualizing a starting object distancefunction;

FIG. 16B is a portion for visualizing and changing the parameter of acorrection function;

FIG. 16C is a portion for visualizing the modified starting objectdistance function;

FIGS. 17A-17D a further example of an adjustment of a starting objectdistance function to a modified object distance model, wherein

FIG. 17A is a further exemplary starting object distance function;

FIG. 17B is the slope of the starting object distance function;

FIG. 17C is the new object distance function obtained by linearadjustment;

FIG. 17D is the slope of the new object distance function;

FIG. 18 an exemplary graphical user interface for visualizing andmodifying the object distance function;

FIG. 19 a further exemplary graphical user interface for visualizing andmodifying the object distance function.

On the abscissa of FIGS. 14A to 17D, the vertical coordinate y of themain line of sight is plotted in mm. On the ordinate of FIGS. 14 to 17,the reciprocal object distance (reciprocal object separation) is plottedin dpt. The coordinate system is the above-described coordinate system{u,y}.

DETAILED DESCRIPTION

FIG. 1 shows the starting target astigmatism distribution based on apredetermined starting surface for an addition of 2.5 dpt. The maximumastigmatism for the periphery is 2.6 dpt. Based on the starting targetastigmatism distribution, a spectacle lens with the followingprescription values and parameters is to be calculated: sphere(sph)=−5.0 dpt; cylinder (cyl)=0.0 dpt; addition (add)=2.5 dpt; basecurve (BC)=3.0 dpt; refractive index n=1.579. The spectacle lens iscalculated in a wearing position with the parameters: corneal vertexdistance (CVD)=13 mm; forward inclination (FI)=7°; interpupillarydistance (ID)=64 mm; Y tilt angle=0°.

In one example, a factor k=0.58 is determined depending on theprescription data of the spectacle lens (in particular the prescriptionastigmatism, the prescribed axis of the prescription astigmatism, andthe prescribed addition) and the tilt angle of the spectacle lens (cf.equations (7) to (13)). The factor k=0.58 is multiplied by the maximumtemporal astigmatism of the starting target astigmatism distribution.Subsequently, an interpolation of the target astigmatism values betweenthe 0.5 dpt base target isoastigmatism line and the periphery of thespectacle lens is performed taking the maximum temporal astigmatismmultiplied by the factor k into consideration. The interpolation isperformed for the peripheral target astigmatism according to thetruncated cone method described in DE 10 2009 005 206 or DE 10 2009 005214.

In this example, the multiplication of the maximum temporal astigmatismby the factor k does not have any influence on the 0.5 dpt base targetisoastigmatism line. The target astigmatism values between the main lineand the 0.5 dpt base target isoastigmatism line thus remain unchanged.Between the temporal 0.5 dpt base target isoastigmatism line and thepeak of the temporal astigmatism hill (i.e. the position of the maximumtarget astigmatism), however, an interpolation on the basis of thescaled maximum temporal astigmatism (in this case 2.6*0.58=1,508 dpt) isperformed. FIG. 2 shows the target astigmatism distribution obtainedafter a multiplication of the maximum temporal astigmatism and asubsequent interpolation. The asymmetric target astigmatism distributionshown in FIG. 2 applies to a progressive spectacle lens having anaddition of 2.5 dpt.

As described in DE 10 2008 015 189, the total astigmatism specificationresulting from a multiplication of the maximum temporal targetastigmatism with subsequent interpolation of the target astigmatismvalues could be scaled depending on the addition as a whole, in order toobtain target astigmatism specifications for a different addition. Forexample, the target astigmatism distribution shown in FIG. 2 can bescaled with the factor 0.3 as a whole to obtain a new addition of 0.75from the original addition of 2.5 dpt. Thereby, a temporal maximumastigmatism of 1.508*0.3=0.45 results. The target astigmatismdistribution additionally scaled depending on the addition is shown inFIG. 3.

FIG. 4 shows a comparative example of a target astigmatism distributionobtained from the target astigmatism distribution shown in FIG. 1 bymeans of a (global) scaling depending on the addition (as described inDE 10 2008 015 189). The example shown in FIG. 4 corresponds to arescaling of the starting target astigmatism distribution from theoriginal addition of 2.5 dpt to a new addition of 0.75 dpt.

FIG. 5 shows a portion of a graphical user interface, which makes itpossible to set the prefactor v. As described above, the asymptoticprefactor v can be specified e.g. depending on the mean distance powerby a double asymptote function (cf. equation 7) with the parametersa=0.475; b=0.525; c=−5.0; d=3.5 and m=1.

FIGS. 6A, B to 12A, B show the change of the target objectives in anexemplary transformation of the temporal target astigmatism distribution(FIGS. 6A and 6B) as well as the change of the results of theoptimization of a progressive spectacle lens according to the respectivetarget astigmatism objectives. The parameters of the prescription are asfollows:

-   -   sphere (sph)=−8 dpt;    -   cylinder (cyl)=6 dpt;    -   axis 45°;    -   addition 0.75 dpt.

The tilt angle, which in the case of flat base curves approximatelycorresponds to the face form angle, is 5°.

According to the above-described formulae (7) to (14), a factor k with avalue of 0.58 results.

Figs. X-A (X=6, 7, . . . 12) relate to a comparative example with asymmetric target astigmatism distribution (“starting target astigmatismdistribution”). Figs. X-B (X=6, 7, . . . , 12) relate to an embodimentaccording to an aspect of the invention (“manipulated targetobjectives”) with a non-symmetric target astigmatism distribution.

The target astigmatism distribution shown in FIG. 6B is obtained fromthe symmetric target astigmatism distribution shown in FIG. 6A by amultiplication of the temporal target astigmatism by the factor k=0.58and a subsequent interpolation of the target astigmatism values. Theinterpolation is performed according to the truncated cone modeldisclosed in DE 10 2009 005 206 or DE 10 2009 005 214 for the peripheralastigmatism. The nasal target astigmatism is not affected by thismodification. Consequently, the maximum temporal target astigmatism islower than the maximum nasal target astigmatism by the factor 0.58.

FIGS. 7A to 10A show the surface properties of the progressive surfaceof a spectacle lens optimized according to the symmetric targetastigmatism objectives shown in FIG. 6A. FIGS. 7B to 10B show thesurface properties of the progressive surface of a spectacle lensoptimized according to the asymmetric manipulated target objectivesshown in FIG. 6B. FIGS. 11A, B and 12A, B each show the astigmatism(FIGS. 11A, B) and the refractive power (FIGS. 12A, B) in the wearingposition of the respective progressive spectacle lens. The followingtable 1 lists the target objectives and properties, shown in FIGS. 6A, Bto 12A, B, of a progressive surface optimized on the basis of therespective target objectives.

TABLE 1 Symmetric Manipulated target target Property shown objectivesobjectives Target astigmatism [dpt] FIG. 6A FIG. 6B Surface power of theprogressive surface FIG. 7A FIG. 7B [dpt] Surface power gradient of theprogressive FIG. 8A FIG. 8B surface [dpt/mm] Surface astigmatism of theprogressive FIG. 9A FIG. 9B surface [dpt] Surface astigmatism gradientof the FIG. 10A FIG. 10B progressive surface [dpt/mm] Wearing positionastigmatism [dpt] FIG. 11A FIG. 11B Mean refractive power in wearingposition FIG. 12A FIG. 12B [dpt]

A comparison of FIGS. 6A and 6B clearly shows the asymmetry of themanipulated target astigmatism distribution shown in FIG. 6B. In FIG.6B, the temporal target astigmatism is below 0.5 dpt.

The progressive surface of the spectacle lens optimized according to themanipulated target objectives shown in FIG. 6B has clearly less surfacepower modifications temporally (cf. also FIG. 8A and FIG. 8B). Forexample, in a comparison of the gradients of the surface power of theprogressive surface shown in FIG. 8A and FIG. 8, it can be clearly seenthat the progressive surface optimized according to the manipulatedtarget astigmatism objectives temporally has substantially smallergradients than the surface optimized according to the symmetric targetastigmatism objectives. In this example, the gradients are smaller by afactor 5.

Moreover, a comparison of FIGS. 9A and 9B with FIGS. 10A and 10B showsthat the progressive surface optimized according to the manipulatedtarget astigmatism objectives temporally has clearly less modificationsof the surface astigmatism and thus clearly smaller gradients of thesurface astigmatism than the surface optimized according to thesymmetric target astigmatism objectives. In this example, the gradientsare smaller by a factor 4.5.

Also, the properties in the wearing position (astigmatism and refractivepower in the wearing position) of the spectacle lens optimized accordingto manipulated target astigmatism objectives have clearly lessgradients, wherein the central viewing zones do not differ substantiallyin size and usability. In the specific example, the gradients changefrom 0.45 dpt/mm to 0.05 dpt/mm. For the mean refractive power in thewearing position, a reduction from 0.55 dpt/mm (cf. FIG. 12A) to 0.15dpt/mm (cf. FIG. 12B) will be obtained.

FIGS. 13A and 13B schematically show the image formation of objects atdifferent object distances (object separations) through a spectacle lens10. The spectacle lens 10 is disposed in a predetermined wearingposition in front of the eyes 12 of the spectacles wearer. In FIGS. 13Aand 13B:

-   a1=1/A₁ is the object distance (object separation);-   e is the corneal vertex distance (CVD);-   b′ is the ocular center of rotation distance;-   s_(z′) is the distance corneal apex−ocular center of rotation-   s′_(BG) is the image separation/distance;-   Z′ is the ocular center of rotation;-   R is the far point sphere; and-   SK is the vertex sphere.

The calculation and optimization of the spectacle lens 10 is performedcompletely in the wearing position of the spectacle lens 12, i.e. takingthe predetermined arrangement of the spectacle lens in front of the eyes12 of the spectacles wearer (defined by the corneal vertex distance,forward inclination, etc.) and a predetermined object distance modelinto consideration. The object distance model can comprise theobjectives for an object surface 14, which specify different objectdistances or object zones for foveal vision. The object surface 14 ispreferably defined by the objectives for the reciprocal object distance(the reciprocal object separation) A₁(x,y) along the object-side mainrays. The course of the reciprocal object distance A₁(x=x₀, y)=A₁(u=0,y)along the main line of sight (i.e. with x=x₀ and u=0) represents theobject distance function. The object distance functionA₁(x=x₀,y)=A₁(u=0,y) determines the width of the viewing zones in thesurrounding of the main line of sight (Minkwitz theorem). A point on theobject surface is imaged to the far point sphere by the spectacle lens,as is schematically shown in FIGS. 13A and 13B. In the example shown inFIGS. 13A and 13B, the eye-side surface of the spectacle lens 10 is theprogressive surface to be optimized.

According to a first example, the object distance function A₁(y) isrepresented as the sum of two double asymptote functions. FIGS. 14A and14B show an exemplary starting object distance function A_(1G)(y)(broken line) and a transformed object distance function A₁(y) adjustedto the new object distance (solid line), which is obtained by means ofoverlaying the starting object distance function A₁(y) with a correctionfunction A_(1corr)(y) (chain-dotted line).

The parameters of the starting object distance function (which isdescribed by a double asymptote function) are a_(G)=2.606 dpt,b_(G)=−2.588 dpt, c=−0.46/mm, d=2.2 mm and m=0.75.

In this case, the distance reference point DF (design point distance) isat y=+8 mm (y_(DF)=8 mm) and the near reference point DN (design pointnear) is at y=−12 mm (y_(DN)=−12 mm). The object distance in thedistance reference point is infinite and consequentlyA_(1distance)=A_(1G)(y_(DF))=0.00 dpt. The object distance in the nearreference point is 40 cm and consequently A_(1near)=A_(1G)(y_(DN))=−2.50dpt.

The object distances in the distance and near reference points for aspecific spectacles wearer or for other designs and applications may bedifferent from the above standard model though. For example, an objectdistance of −400 cm can be taken into consideration in the distancereference point DF, and an object distance of −50 cm in the nearreference point. In this case, the modified specifications for theobject distance in the distance and near reference points areA_(1distance)=A_(1G)(y_(DF))=−0.25 dpt andA_(1near)=A_(1G)(y_(DN))=−2.00 dpt, respectively.

By overlaying the starting object distance function A_(1G)(y) with acorrection function A_(1corr)(y) with the same coefficients c, d and mas that of the starting object distance function and with thecoefficients b_(corr)=0.526 and a_(corr)=−0.782, the adjusted course ofthe object distance function A₁(y) shown in FIG. 14B results.

FIG. 15A shows a further exemplary starting object distance functionA_(1G)(y). FIG. 15B shows the slope of the starting object distancefunction (i.e. the derivative of the starting object distance functionaccording to y). The starting object distance function is described by adouble asymptote function with the coefficients a_(G)=2.100;b_(G)=2.801; c=0.206; d=5.080; m=0.5. The starting object distancefunction has a very smooth transition from the distance to the nearportions. In this example, the reciprocal object distance A_(1Gdistance)in the distance reference point DF (at y=10 mm) is equal to −1.00 dpt(A_(1Gdistance)=−1.00 dpt), and the reciprocal object distanceA_(1Gnear) in the near reference point DN (at y=−14 mm) is equal to −2.5dpt (A _(1Gnear)=−2.5 dpt). Thus, the starting object distance functiondescribes a tube design for a near-vision lens.

FIG. 15C shows an exemplary Gaussian function A_(1G)(y) (i.e. thecorrecting reciprocal object distance along the main line of sight),which can be used for modifying the design characteristic, for example.The Gaussian function shown in FIG. 15C is described by a Gaussian bellcurve

${g(y)} = {g_{a} + {g_{b}{\mathbb{e}}^{- \frac{y - y_{0}}{\sigma}}}}$with the coefficients g_(a)=0.00; g_(b)=0.35; σ=5.56 and y₀=−3.47. FIG.15D shows the slope (first derivative according to y) of the Gaussianbell curve shown in FIG. 15C.

FIG. 15E shows an object distance function A₁(y) (i.e. the modifiedreciprocal object distance along the main line of sight), which isobtained by overlaying the starting object distance function shown inFIG. 15A with the Gaussian function shown in FIG. 15C. FIG. 15F showsthe slope (the first derivative according to y) of the object distancefunction A₁(y) shown in FIG. 15E. By overlaying the starting objectdistance function with the Gaussian bell curve shown in FIG. 15C, amodified object distance function is obtained, which is particularlysuitable for a for a lens design for computer work. The slope of themodified object distance function A₁(y) has a maximum at y=−7 mm, i.e.the modification of the object distance function A₁(y) is greatestthere. Accordingly, at a height of y=−7 mm there is located thenarrowest point in the progression range with respect to the viewingzone width, which is e.g. defined by the 0.5 dpt isoastigmatism line. Ata height of y=0 mm, the slope of the object distance function A₁(y) hasa local minimum. At this height, the viewing zone is relatively wide andcan be used for viewing at screens.

Moreover, the object distance function A₁(y) shown in FIG. 15E can beadjusted to the modified specifications for the object distance in thedistance reference point and in the near reference point. FIG. 15G showsa modified object distance function A_(1new)(y) obtained by adjustingthe object distance function A₁(y) shown in FIG. 15E to the objectives

-   A ₁(y=10)=−0.50 dpt and-   A ₁(y=14)=−2.50 dpt.

The modified and adjusted object distance function is obtained accordingto the formula A_(1new)(y)=c+(1+m)A₁(y), where c=0.836 and m=0.335.

FIG. 15H shows the slope (derivative according to y) of the modifiedobject distance function A_(1new)(y) shown in FIG. 15G.

FIG. 16A shows a portion of a graphical user interface, wherein theportion is adapted to visualize the starting object distance function(in the specific case a starting object distance function A_(1G)(y) inthe form of a double asymptote function of the form

$\left. {{A_{1\; G}(y)} = {b + \frac{a}{\left( {1 + {\mathbb{e}}^{{c{({y + d})}}m}} \right.}}} \right).$The graphical user interface can further comprise a portion (not shownin FIG. 16A) having a fields for inputting and optionally modifying thecoefficients of the starting object distance function.

FIG. 16B shows a graphical user interface adapted to visualize acorrection function (in this case a Gaussian bell curve of the form

$\left. {A_{1\;{Gauss}} = {a_{0} + {b_{0}{\mathbb{e}}^{- {(\frac{y - y_{0}}{\sigma})}^{2}}}}} \right).$Moreover, the graphical user interface comprises a further portionhaving input fields/masks in which the coefficients of the correctionfunction are indicated and optionally changed. By the overlay with acorrection function in the form of a Gaussian bell curve, theintermediate zone can be weighted new. FIG. 16C shows a graphical userinterface with a portion adapted to visualize the object distancefunction put together by overlaying the starting object distancefunction with the correction function.

FIGS. 17A and 17B show the course and the derivative of an exemplarystarting object distance function (basic function):

-   -   FIG. 17A shows the course of the function A_(1G)(y) along the        main line in dpt;    -   FIG. 17B shows the first derivative

$\frac{\mathbb{d}{A_{1G}(y)}}{\mathbb{d}y}$

-   -    along the main line.

In this example, the wearer specifications for the desired objectdistances are A_(1distance)=−0.5 dpt at the height y_(F)=12 mm andA_(1near)=−2.75 dpt at the height y_(N)=−14 mm. The actual values of thestarting object distance function A_(1G)(y) in the reference pointresult for A_(1G)(y_(F))=−0.8896 dpt and A_(1G)(y_(N))=−2.4721 dpt.

The starting object distance function shown in FIG. 17A is transformedlinearly, wherein the straight line coefficients are calculateddepending on the modified specifications for the object distances in thedistance and near reference points as c=0.7648 and m=0.4212.

FIGS. 17C and 17D show the course and the derivative of the newtransformed object distance function A₁ (A₁−function), where:

-   -   FIG. 17C shows the course of the new object distance function        A₁(y) along the main line on the front surface of the spectacle        lens; and    -   FIG. 17D shows the derivative

$\frac{\mathbb{d}{A_{1}(y)}}{\mathbb{d}y}$

-   -    of the new object distance function A₁(y) along the main line        on the front surface of the spectacle lens.

FIGS. 18 and 19 show an exemplary mask and an exemplary graphical userinterface, respectively for indication and optionally modifying theparameters of the object distance function and for visualizing the thuscalculated object distance function.

REFERENCE NUMERAL LIST

-   10 spectacle lens-   12 eye of the spectacles wearer-   14 object surface-   e corneal vertex distance (CVD)-   b′ ocular center of rotation distance-   sZ′ distance corneal vertex−ocular center of rotation-   s′BG image distance-   Z′ ocular center of rotation-   R far point sphere-   SK vertex sphere

The invention claimed is:
 1. A computer-implemented method foroptimizing and forming an optimized progressive spectacle lens,comprising: specifying a starting target astigmatism distributionAst_(target) _(start) for the progressive spectacle lens; determining atransformed target astigmatism distribution Ast_(target) _(new) , andoptimizing the progressive spectacle lens on the basis of thetransformed target astigmatism distribution, wherein determining atransformed target astigmatism distribution Ast_(target) _(new)comprises: multiplying the value of the maximum temporal targetastigmatism max ₁₃ Ast_(target—)temporal_(start) of the starting targetastigmatism distribution Ast_(target) _(start) by a factor k: max_Ast_(target—)temporal_(new)=k* max_Ast_(target—)temporal_(start),whereby a modified maximum temporal astigmatismmax_Ast_(target—)temporal_(new) results, wherein the factor k is afunction of at least one prescription value and/or of at least oneparameter of the spectacle lens or its arrangement in front of the eyesof the spectacles wearer, and transforming the starting targetastigmatism distribution Ast_(target) _(start) to the transformed targetastigmatism distribution Ast_(target) _(new) on the basis of themodified maximum temporal astigmatism max _Ast_(target—)temporal_(new),wherein it holds for the factor k that: k=(1−g_(prescription)−h), whereg_(prescription) is a function of at least one prescription value, and his a function of at least one parameter of the spectacle lens or itsarrangement in front of the eyes of the spectacles wearer.
 2. Acomputer-implemented method for optimizing and forming an optimizingprogressive spectacle lens, comprising: specifying a starting targetastigmatism distribution Ast_(target) _(start) for the progressivespectacle lens: determining a transformed target astigmatismdistribution Ast_(target) _(new) , and optimizing the progressivespectacle lens on the basis of the transformed target astigmatismdistribution, wherein determining a transformed target astigmatismdistribution Ast_(target) _(new) comprises: multiplying the value of themaximum temporal target astigmatism max_Ast_(target—)temporal_(start) ofthe starting target astigmatism distribution Ast_(target) _(start) by afactor k: max_Ast_(target—)temporal_(new)=k*max_Ast_(target—)temporal_(start), whereby a modified maximum temporalastigmatism max_Ast_(target—)temporal_(new) results, wherein the factork is a function of at least one prescription value and/or of at leastone parameter of the spectacle lens or its arrangement in front of theeyes of the spectacles wearer, and transforming the starting targetastigmatism distribution Ast_(target) _(start) to the transformed targetastigmatism distribution Ast_(target) _(new) on the basis of themodified maximum temporal astigmatism max_Ast_(target—)temporal_(new),wherein it holds for the factor k that: k=v*(1−g_(prescription)−h),wherein it holds for the factor k that: g_(prescription) is a functionof at least one prescription value; h is a function of at least oneparameter of the spectacle lens or its arrangement in front of the eyesof the spectacles wearer; and V is a prefactor, which is a function ofthe prescription and/or of the base curve of the spectacle lens and/orof the curvature of the back surface of the spectacle lens.
 3. Themethod according to claim 2, wherein the prefactor v is a doubleasymptote function of the distance prescription and/or of the base curveof the spectacle lens and/or of the curvature of the back surface of thespectacle lens.
 4. The method according to claim 1, whereing_(prescription) is the function of the prescription astigmatism:${{g_{prescription} \approx f_{({{prescription}\mspace{14mu}{astigmatism}})}} = \frac{{prescription}\mspace{14mu}{astigmatismn}}{b}},$where the parameter b is in the range of 2 to
 6. 5. The method accordingto claim 1, wherein g_(prescription) is a function of the cylinder axisposition:g _(prescription)≈ƒ_((cylinder axis position))=a* sin³(2* cylinder axisposition), where the parameter a is in the range of 0.05 to 1.0.
 6. Themethod according to claim 1, wherein g_(prescription) is a linearfunction of the addition:ƒ_((addition))=c* addition+d , where the parameter c is in the rangebetween 0 and −1, and the parameter d is in the range of 2.0 to
 0. 7.The method according to claim 1, wherein h is a function of the tiltangle of the spectacle lens:${{h \approx f_{({{tilt}\mspace{14mu}{angle}})}} = \frac{{tilt}\mspace{14mu}{angle}}{g}},$where the parameter g is in the range of 50 to
 500. 8. The methodaccording to claim 1, wherein transforming the starting targetastigmatism distribution Ast_(target) _(start) on the basis of themodified maximum temporal astigmatism max_Ast_(target—)temporal_(new)comprises an interpolation of the target astigmatism values between apredetermined base target isoastigmatism line and the periphery of thespectacle lens taking the modified maximum temporal astigmatism max₁₃Ast_(target—)temporal_(new) into account.
 9. A computer program productadapted, when loaded and executed on a computer, to perform a method foroptimizing a progressive spectacle lens according to claim
 1. 10. Astorage medium with a computer program stored thereon, the computerprogram being adapted, when loaded and executed on a computer, toperform a method for optimizing a progressive spectacle lens accordingto claim
 1. 11. A device for optimizing a progressive spectacle lens,comprising optimizing means adapted to perform an optimization of thespectacle lens according to the method of claim
 1. 12. A method forproducing a progressive spectacle lens, comprising: optimizing thespectacle lens according to the method of claim 1, providing surfacedata of the calculated and optimized spectacle lens; and manufacturingthe spectacle lens according to the provided surface data of thespectacle lens.
 13. A device for producing a progressive spectacle lens,comprising: optimizing means adapted to perform an optimization of thespectacle lens according to the method of claim 1; and processing meansfor finishing the spectacle lens.
 14. The method according to claim 4,wherein g_(prescription) is the function of the prescriptionastigmatism:${{g_{prescription} \approx f_{({{prescription}\mspace{14mu}{astigmatism}})}} = \frac{{prescription}\mspace{14mu}{astigmatismn}}{b}},$where the parameter b is in the range of 4 to
 6. 15. The methodaccording to claim 5, wherein g_(prescription) is a function of thecylinder axis position:g _(prescription) ≈ƒ_((cylinder axis position))=a* sin³(2* cylinder axisposition), where the parameter a is in the range of 0.3 to 0.6.
 16. Themethod according to claim 6, wherein g_(prescription) is a linearfunction of the addition:ƒ_((addition))=c* addition+d , where the parameter c is in the rangebetween −0.75 and −0.3, and the parameter d is in the range between 2and
 1. 17. The method according to claim 7, wherein h is a function ofthe tilt angle of the spectacle lens:${{h \approx f_{({{tilt}\mspace{14mu}{angle}})}} = \frac{{tilt}\mspace{14mu}{angle}}{g}},$where the parameter g is in the range of 100 to
 300. 18. The methodaccording to claim 1, further comprising: forming the optimizedprogressive spectacle lens based on the transformed target astigmatismdistribution Ast_(target) _(new) .